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Beliebt Rechnen >

(x+y)^2dx+(2xy+x^2-8)dy=0

Lösung

(x + y)^{2} d x + (2 x y + x^{2} - 8) d y = 0

Lösung

y = \frac{24 - 3 x ^{2} + 576 - 144 x ^{2} - 3 x ^{4} + 36 c _{1} x}{6 x}, y = \frac{24 - 3 x ^{2} - 576 - 144 x ^{2} - 3 x ^{4} + 36 c _{1} x}{6 x}

Schritte zur Lösung

(x + y)^{2} d x + (2 x y + x^{2} - 8) d y = 0

Solve exact ODE:

y = \frac{24 - 3 x ^{2} + 576 - 144 x ^{2} - 3 x ^{4} + 36 c _{1} x}{6 x}, y = \frac{24 - 3 x ^{2} - 576 - 144 x ^{2} - 3 x ^{4} + 36 c _{1} x}{6 x}

y = \frac{24 - 3 x ^{2} + 576 - 144 x ^{2} - 3 x ^{4} + 36 c _{1} x}{6 x}, y = \frac{24 - 3 x ^{2} - 576 - 144 x ^{2} - 3 x ^{4} + 36 c _{1} x}{6 x}

Graph

Beliebte Beispiele

limit as x approaches 0 of (3x+1)/(7x)

x \to 0 lim (\frac{3 x + 1}{7 x})

integral of (x-1)^2*x^3*(2-x)

\int (x - 1)^{2} \cdot x^{3} \cdot (2 - x) d x

(dy)/(dx)=(5x)/(9y)

\frac{d y}{d x} = \frac{5 x}{9 y}

derivative of 7e^e

\frac{d}{d x} (7 e^{e})

(\partial)/(\partial x)((x^3+y^2)^{1/2})

\frac{\partial}{\partial x} ((x^{3} + y^{2})^{\frac{1}{2}})